Galerkin time-stepping methods for nonlinear parabolic equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 2, p. 261-289

We consider discontinuous as well as continuous Galerkin methods for the time discretization of a class of nonlinear parabolic equations. We show existence and local uniqueness and derive optimal order optimal regularity a priori error estimates. We establish the results in an abstract Hilbert space setting and apply them to a quasilinear parabolic equation.

DOI : https://doi.org/10.1051/m2an:2004013
Classification:  65M15,  65M50
Keywords: nonlinear parabolic equations, local Lipschitz condition, continuous and discontinuous Galerkin methods, a priori error analysis, monotone operators
@article{M2AN_2004__38_2_261_0,
     author = {Akrivis, Georgios and Makridakis, Charalambos},
     title = {Galerkin time-stepping methods for nonlinear parabolic equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {2},
     year = {2004},
     pages = {261-289},
     doi = {10.1051/m2an:2004013},
     zbl = {1085.65094},
     mrnumber = {2069147},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2004__38_2_261_0}
}
Akrivis, Georgios; Makridakis, Charalambos. Galerkin time-stepping methods for nonlinear parabolic equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 2, pp. 261-289. doi : 10.1051/m2an:2004013. http://www.numdam.org/item/M2AN_2004__38_2_261_0/

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